# remainder, remainderf, remainderl

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< c‎ | numeric‎ | math

Defined in header ``<math.h>`` |  |
float remainderf( float x, float y ); | (1) | (since C99)
double remainder( double x, double y ); | (2) | (since C99)
long double remainderl( long double x, long double y ); | (3) | (since C99)
Defined in header ``<tgmath.h>`` |  |
#define remainder( x, y ) | (4) | (since C99)

1-3) Computes the IEEE remainder of the floating-point division operation x/y.
4) Type-generic macro: If any argument has type long double, `remainderl` is called. Otherwise, if any argument has integer type or has type double, `remainder` is called. Otherwise, `remainderf` is called.

The IEEE floating-point remainder of the division operation x/y calculated by this function is exactly the value x - n * y, where the value `n` is the integral value nearest the exact value x/y. When |n-x/y| = ½, the value `n` is chosen to be even.

In contrast to fmod(), the returned value is not guaranteed to have the same sign as x.

If the returned value is ​0​, it will have the same sign as x.

### Parameters

x, y | - | floating-point values

### Return value

If successful, returns the IEEE floating-point remainder of the division x/y as defined above.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result is returned.

If y is zero, but the domain error does not occur, zero is returned.

### Error handling

Errors are reported as specified in `math_errhandling`.

Domain error may occur if y is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- The current rounding mode has no effect.
- FE_INEXACT is never raised, the result is always exact.
- If x is ±∞ and y is not NaN, NaN is returned and FE_INVALID is raised.
- If y is ±0 and x is not NaN, NaN is returned and FE_INVALID is raised.
- If either argument is NaN, NaN is returned.

### Notes

POSIX requires that a domain error occurs if x is infinite or y is zero.

fmod, but not `remainder` is useful for doing silent wrapping of floating-point types to unsigned integer types: (0.0 <= (y = fmod(rint(x), 65536.0)) ? y : 65536.0 + y) is in the range `[`-0.0`,` 65535.0`]`, which corresponds to unsigned short, but remainder(rint(x), 65536.0) is in the range `[`-32767.0`,` +32768.0`]`, which is outside of the range of signed short.

### Example

Run this code

    #include <fenv.h>
    #include <math.h>
    #include <stdio.h>
    // #pragma STDC FENV_ACCESS ON

    int main(void)
    {
        printf("remainder(+5.1, +3.0) = %.1f\n", remainder(5.1, 3));
        printf("remainder(-5.1, +3.0) = %.1f\n", remainder(-5.1, 3));
        printf("remainder(+5.1, -3.0) = %.1f\n", remainder(5.1, -3));
        printf("remainder(-5.1, -3.0) = %.1f\n", remainder(-5.1, -3));

        // special values
        printf("remainder(-0.0, 1.0) = %.1f\n", remainder(-0.0, 1));
        printf("remainder(+5.1, Inf) = %.1f\n", remainder(5.1, INFINITY));

        // error handling
        feclearexcept(FE_ALL_EXCEPT);
        printf("remainder(+5.1, 0) = %.1f\n", remainder(5.1, 0));
        if (fetestexcept(FE_INVALID))
            puts("    FE_INVALID raised");
    }

Output:

    remainder(+5.1, +3.0) = -0.9
    remainder(-5.1, +3.0) = 0.9
    remainder(+5.1, -3.0) = -0.9
    remainder(-5.1, -3.0) = 0.9
    remainder(+0.0, 1.0) = 0.0
    remainder(-0.0, 1.0) = -0.0
    remainder(+5.1, Inf) = 5.1
    remainder(+5.1, 0) = -nan
        FE_INVALID raised

### References

- C23 standard (ISO/IEC 9899:2024):

  - 7.12.10.2 The remainder functions (p: TBD)

  - 7.25 Type-generic math <tgmath.h> (p: TBD)

  - F.10.7.2 The remainder functions (p: TBD)

- C17 standard (ISO/IEC 9899:2018):

  - 7.12.10.2 The remainder functions (p: 185-186)

  - 7.25 Type-generic math <tgmath.h> (p: 272-273)

  - F.10.7.2 The remainder functions (p: 385)

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.10.2 The remainder functions (p: 254-255)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.7.2 The remainder functions (p: 529)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.10.2 The remainder functions (p: 235)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.7.2 The remainder functions (p: 465)

### See also

divldivlldiv (C99) | computes quotient and remainder of integer division (function)
fmodfmodffmodl (C99)(C99) | computes remainder of the floating-point division operation (function)
remquoremquofremquol (C99)(C99)(C99) | computes signed remainder as well as the three last bits of the division operation (function)
C++ documentation for remainder

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